1. Caveats and Comments
1
Overview:
This is my analysis, not Stanfordโs. My goal is to understand the trajectory of COVID. It is not confidential and can be freely shared. The R program code is
available at https://github.com/StevenLShafer/COVID19/. The daily analysis are available at https://1drv.ms/u/s!AuOyHP_aTIy7rowrt2AjGpWm_frnEQ?e=KBcNbh.
You are welcome to use the R code on GitHub for any purpose.
I am attempting to keep the analysis and commentary apolitical. I am now including partisan lean as a metric to help understand the epidemic. I occasionally point
out misrepresentations by government officials. I occasionally point out where government recommendations have placed Americans at increasing risk.
I try to provide a daily update in the morning, except Sundays. My analysis my be delayed by my clinical responsibilities as a Stanford anesthesiologist.
There is a lot of information on the figures. If something isnโt clear, please see the explanation on slide 2.
Data sources:
โข USA Case Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv
โข USA Death Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_US.csv
โข USA Testing and Hospitalization Data: https://raw.githubusercontent.com/COVID19Tracking/covid-tracking-data/master/data/states_daily_4pm_et.csv
โข Global Case Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv
โข Global Death Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv
โข Global Testing Data: https://raw.githubusercontent.com/owid/covid-19-data/master/public/data/owid-covid-data.csv
โข Mobility Data: https://www.gstatic.com/covid19/mobility/Global_Mobility_Report.csv
โข Partisan Lean: MIT Election Data and Science Lab: https://doi.org/10.7910/DVN/VOQCHQ/HEIJCQ
โข Ensemble Model: https://github.com/reichlab/covid19-forecast-hub/raw/master/data-processed/COVIDhub-ensemble/2020-xx-xx-COVIDhub-ensemble.csv
Models:
1. Future projections of case numbers are based on the Gompertz function (https://en.wikipedia.org/wiki/Gompertz_function): log ๐๐ข๐๐ข๐๐๐ก๐๐ฃ๐ ๐๐๐ ๐๐ =
๐๐ข๐๐๐๐๐ก ๐๐๐ ๐๐ + ๐๐๐ฅ๐๐๐ข๐ ๐๐๐ ๐๐ โ ๐๐ข๐๐๐๐๐ก ๐๐๐ ๐๐ 1 โ ๐โ๐ ๐ก . This is a naรฏve asymptotic model. k is the rate constant, such that log(2) / k = time to 50%
rise. t is the number of days. Wikipedia The Gompertz function is estimated from the last 3 weeks of data for cumulative cases (red dots in the figures).
Deaths are predicted from a log linear regression of deaths over the past 21 days. For the US, and individual states, I am also including the 98% prediction
interval from the COVID-19 Forecast Hub (https://covid19forecasthub.org/).
2. The rate of change in daily cases and deaths is the slope of delta cases / day over the last 14 days, divided by the average number of cases.
Locations
The locations for the modeling are where Pamela and I have family and friends, locations of interest to friends and colleagues, or countries in the news (e.g.,
China, South Korea, Sweden, Brazil) or with significant economic impact on the United States (e.g., Japan, Canada, Mexico). Locations are easy to add.
Stay safe, well, resilient, and kind.
Steve Shafer
steven.shafer@Stanford.edu
2. 2,586,092
152,804
1
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
Actual(points)/Predicted(line)
Phase
Pre-Model
Modeled
Deaths
Tests
USA projection as of 2020-05-27
0
10,000
20,000
30,000
0
2,000
4,000
6,000
Cases/Day
Deaths/Day
Cases: 1,662,302 (32,123) -- Deaths: 98,220 (829) -- Case Mortality: 5.9% -- Daily Change in Cases: -0.5%
Explanation of the Figures
2
Brown dots:
cumulative tests
Red dots: cumulative cases
used to estimate Gompertz
function, presently set to last
3 weeks
Red line: predicted cumulative
cases based on the Gompertz
function estimated from the red
dots
Red number: total cases
on June 30th, based on
the Gompertz function
estimated from the red
dots
Black number: total
Deaths on July 31th,
based on log-linear
regression of the past
21 days
Black line: predicted
cumulative deaths, based
on a log linear regression
of deaths over past 21
days.
Axis for deaths / day, usually
1/10th of the axis for cases /
day on the left side of the
figure.
Green line: linear regression
over 8 days, used to calculate
percent increase / decrease
(see below)
Daily change in cases,
calculated as the slope of the
green line (above left) /
number of new cases
yesterday.
Case mortality:
cumulative deaths
/ cumulative cases.
Cases / day calculated
from cumulative cases
used to estimate the
Gompertz function
Cases / day calculated
from cumulative cases
not used to estimate the
Gompertz function
Deaths / day,
axis is on the left
Blue line: today
Blue dots: cumulative cases not
used to estimate Gompertz
function
Cumulative cases
(yesterdayโs cases)
and cumulative deaths
(yesterdayโs deaths)
Axis for cases / day.
Axis for deaths / day
appears to the right.
Geographic
location
Date of analysis,
also shown as
blue vertical line
below
Purple wedge: 98% ensemble
prediction interval from COVID-19
Forecast Hub (USA and US
States only)
9. Average new cases over past 7 days
PER
ARG
ISR
COL
BRA
ESP
USA
IRQ
BOL
CHL
HND
FRA
PRY
GTM
IND
LBY
ECU
DOM
ROU
ZAF
MEX
UKR
BEL
PHL
SAU
MAR
CHE
NLD
RUS
CZE
AUT
IRN
NPL
VEN
SLV
KGZ
PRT
GRC
ITA
GBR
POL
BGR
AZE
BLR
ETH
SWE
TUR
SRB
DEU
BGD
DNK
ZMB
UZB
SVK
CAN
RWA
KAZ
DZA
TUN
IDN
SEN
JOR
KOR
KEN
AUS
USA
None
1 in 20,000
1 in 10,000
1 in 6,667
1 in 5,000
1 in 4,000
1 in 3,333
1 in 2,857
1 6 11 16 21 26 31 36 41 46 51 56 61 66
Rank
Averagecases/day
Average new cases over past 7 days
Excludes countries with population < 5,000,000
2020-08-29 Summary: 9
12. Average daily deaths over past 7 days
COL
BOL
PER
ARG
MEX
BRA
CHL
HND
USA
ZAF
ECU
IRQ
ROU
PRY
GTM
IRN
DOM
ISR
BGR
SAU
SLV
LBY
MAR
KAZ
IND
AUS
UKR
RUS
ESP
PHL
BLR
ZWE
IDN
SRB
FRA
PRT
TUR
POL
NPL
BGD
GRC
DZA
AZE
VEN
NLD
UZB
EGY
CAN
ETH
GBR
SEN
KEN
CZE
TUN
SYR
AGO
ITA
YEM
CHE
ZMB
JPN
NIC
SWE
MWI
JOR
USA
None
1 in 500,000
1 in 250,000
1 in 166,667
1 in 125,000
1 6 11 16 21 26 31 36 41 46 51 56 61 66
Rank
Averagedeaths/day
Average daily deaths over past 7 days
Excludes countries with population < 5,000,000
2020-08-29 Summary: 12
14. Change in New Cases per Day
New cases are:
Increasing > +3%
Increasing between +1% and +3%
No Change (-1% to +1%)
Decreasing between -1% and -3%
Decreasing > -3%
New cases by state as of 2020-08-29
2020-08-29 Summary: 14
15. Cases as a Percent of Peak Cases
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
PercentofPeak
Daily Cases as a Percent of Peak Cases
2020-08-29 Summary: 15
16. Change in New Deaths per Day
New deaths are:
Increasing > +0.5%
Increasing between +0.1% and +0.5%
No Change (-0.1% to +0.1%)
Decreasing between -0.1% and -0.5%
Decreasing > -0.5%
New deaths by state as of 2020-08-29
2020-08-29 Summary: 16
17. Deaths as a Percent of Peak Deaths
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
PercentofPeak
Daily Deaths as a Percent of Peak Deaths
2020-08-29 Summary: 17
18. Change in cases vs change in deaths
AL
AK
AZ
AR
CA
CO
CT
DE
DC
FL
GA
HI
ID
IL
IN
IA
KS
KY
LA
ME
MD
MA
MI
MN
MS
MO
MT
NE
NV
NH
NJ
NM
NY NC
ND
OH
OK
OR
PA
RI
SC
SD
TN
TX
UT
VT
VA
WA
WV
WI
WY
-6
-3
0
3
6
-10 -5 0 5 10
Change in cases (%/day)
Changeindeaths(%/day)
Change in cases vs change in deaths over last 14 days as of 2020-08-29
2020-08-29 Summary: 18
19. Total US COVID-19 Cases
CA
TX
FL
NY
GA
IL
AZ
NJ
NC
TN
LA
PA
MA
AL
OH
VA
SC
MI
MD
IN
MO
MS
WI
WA
MN
NV
IA
AR
CO
OK
CT
UT
KY
KS
NE
ID
OR
NM
RI
DE
DC
SD
ND
WV
HI
NH
MT
AK
ME
WY
VT
0
200,000
400,000
600,000
800,000
1 6 11 16 21 26 31 36 41 46 51
Rank
Totalcases
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Cases
p masks as of July 20, 2020: 0.41, p governor: 0.79. NB: association != causation.
2020-08-29 Summary: 19
20. Total US COVID-19 Cases
LA
FL
AZ
MS
GA
AL
SC
NY
TN
NV
NJ
TX
RI
IA
AR
DC
MA
IL
CA
MD
ID
DE
NE
UT
NC
CT
ND
OK
SD
KS
VA
IN
MO
MN
WI
NM
MI
PA
KY
OH
CO
WA
AK
MT
WY
OR
HI
WV
NH
ME
VT
None
1 in 200
1 in 100
1 in 67
1 in 50
1 in 40
1 in 33
1 in 29
1 6 11 16 21 26 31 36 41 46 51
Rank
TotalCases
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Cases
p masks as of July 20, 2020: 0.86, p governor: 0.12. NB: association != causation.
2020-08-29 Summary: 20
21. Average US COVID-19 cases over the past
7 days
IA
ND
SD
AL
MS
KS
GA
TN
AR
MO
OK
HI
NV
TX
SC
IL
ID
FL
NC
IN
LA
KY
CA
NE
MN
WI
MT
UT
VA
AK
RI
MD
OH
MI
DC
AZ
WY
NM
WA
WV
OR
CO
MA
PA
DE
CT
NJ
NY
ME
NH
VT
None
1 in 10,000
1 in 5,000
1 in 3,333
1 6 11 16 21 26 31 36 41 46 51
Rank
NewCases/Day
Masks
No
Yes
Governor
aa
Democratic
Republican
Average US COVID-19 cases over the past 7 days
p masks as of July 20, 2020: 0.01, p governor: 0.01. NB: association != causation.
2020-08-29 Summary: 21
22. Total US COVID-19 Deaths
NY
NJ
CA
TX
FL
MA
IL
PA
MI
GA
AZ
LA
CT
OH
MD
IN
SC
NC
VA
MS
AL
CO
WA
MN
TN
MO
NV
WI
IA
RI
KY
OK
NM
AR
DC
DE
OR
KS
NH
UT
NE
ID
WV
SD
ND
ME
MT
HI
VT
AK
WY
0
10,000
20,000
30,000
1 6 11 16 21 26 31 36 41 46 51
Rank
TotalDeaths
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Deaths
p masks as of July 20, 2020: 0.065, p governor: 0.23. NB: association != causation.
2020-08-29 Summary: 22
23. Total US COVID-19 Deaths
NJ
NY
MA
CT
LA
RI
DC
MS
AZ
MI
IL
DE
MD
PA
SC
GA
FL
IN
TX
AL
NV
NM
OH
IA
CO
MN
CA
NH
VA
NC
AR
WA
TN
MO
KY
NE
OK
ID
WI
SD
ND
KS
UT
WV
OR
ME
MT
VT
WY
AK
HI
None
1 in 2,000
1 in 1,000
1 in 667
1 in 500
1 6 11 16 21 26 31 36 41 46 51
Rank
TotalDeaths
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Deaths
p masks as of July 20, 2020: 0.028, p governor: 0.23. NB: association != causation.
2020-08-29 Summary: 23
24. Average US COVID-19 deaths over the past
7 days
MS
LA
GA
SC
TX
FL
AZ
AR
NV
ID
TN
IA
AL
CA
MA
OK
WV
NC
RI
NM
OH
VA
KY
IL
IN
MN
ND
AK
MT
HI
NE
MD
PA
MO
DE
SD
WA
KS
OR
UT
WI
MI
CO
DC
WY
NY
ME
NH
NJ
CT
VT
None
1 in 500,000
1 in 250,000
1 in 166,667
1 in 125,000
1 in 100,000
1 6 11 16 21 26 31 36 41 46 51
Rank
Deaths/Day
Masks
No
Yes
Governor
aa
Democratic
Republican
Average US COVID-19 deaths over the past 7 days
p masks as of July 20, 2020: 0.49, p governor: 0.018. NB: association != causation.
2020-08-29 Summary: 24
25. Daily testing trends
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
min
max
min
max
min
max
min
max
min
max
min
max
min
max
min
max
Dailytestingfrommintomax
Daily testing trends from min to max
Line = Friedman's supersmoother
2020-08-29 Summary: 25
26. Change in daily tests over past 14 days
MS
ME
MA
HI
VT
NH
TN
WV
NC
MT
MI
VA
OK
AL
CT
IL
AR
KS
IN
WY
NY
KY
RI
OH
IA
NE
DC
MD
SD
NJ
WA
MN
ND
PA
NM
OR
CA
MO
CO
ID
GA
DE
WI
UT
LA
AZ
TX
SC
NV
AK
FL
-4.0
-2.0
0.0
2.0
4.0
1 6 11 16 21 26 31 36 41 46 51
Rank
Changeindailytests(%/day)
Masks
No
Yes
Governor
aa
Democratic
Republican
Change in daily tests over past 14 days
p masks as of July 20, 2020: 0.25, p governor: 0.87. NB: association != causation.
2020-08-29 Summary: 26
28. Percent of Positive COVID Tests
AZ
MS
FL
AL
SC
ID
TX
GA
NV
KS
IA
NE
SD
IN
AR
MO
MD
CO
PA
RI
LA
UT
VA
MA
NC
DE
TN
NJ
MN
OK
WI
CA
IL
KY
ND
OH
NY
WA
WY
DC
OR
CT
MI
HI
NH
NM
MT
WV
ME
AK
VT
0.0
5.0
10.0
15.0
1 6 11 16 21 26 31 36 41 46 51
Rank
PercentofPositiveTests
Masks
No
Yes
Governor
aa
Democratic
Republican
Percent of Positive COVID Tests
p masks as of July 20, 2020: 0.054, p governor: 0.0058. NB: association != causation.
2020-08-29 Summary: 28
29. Positive fraction trends
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
min
max
min
max
min
max
min
max
min
max
min
max
min
max
min
max
Fractionpositivefrommintomax
Positive fraction trends from min to max
2020-08-29 Summary: 29
30. Change in positive tests over past 14 days
HI
ND
SD
MO
KY
MS
IA
OK
AK
NV
WI
SC
TX
KS
ID
UT
MT
MN
OR
FL
NE
NC
AR
CA
AL
IN
GA
CO
WA
TN
VA
WV
LA
NM
PA
IL
AZ
OH
DE
MD
MI
WY
RI
VT
NH
NJ
DC
NY
MA
ME
CT
-1.0
0.0
1.0
2.0
1 6 11 16 21 26 31 36 41 46 51
Rank
Changeinpositivetests(%/day)
Masks
No
Yes
Governor
aa
Democratic
Republican
Change in positive tests over past 14 days
p masks as of July 20, 2020: 0.0062, p governor: 0.078. NB: association != causation.
2020-08-29 Summary: 30
31. Change in tests vs change in positive tests
AL
AK
AZ
AR
CACO
CT
DE
DC
FL
GA
HI
ID
IL
IN
IA
KS
KY
LA
ME
MD
MA
MI
MN
MS
MO
MT
NE
NV
NH
NJ
NM
NY
NC
ND
OH
OK
OR
PA
RI
SC
SD
TN
TXUT
VT
VA
WA
WV
WI
WY
-1
0
1
2
-2 0 2 4
Change in tests (%/day)
Changeinpositivetests(%/day)
Change in tests vs change in positive tests last 14 days as of 2020-08-29
2020-08-29 Summary: 31
32. Current hospitalizations as a percent of peak
since FebruaryAK
HI
KS
MO
MT
ND
WV
WY
OK
KY
AR
NE
ID
NC
IA
VA
GA
OH
SD
TN
MS
AL
IN
NV
CA
WA
SC
MN
OR
WI
UT
FL
LA
TX
IL
RI
NM
VT
AZ
MD
CO
MI
DC
PA
DE
ME
MA
NH
NJ
CT
NY
0
30
60
90
1 6 11 16 21 26 31 36 41 46 51
Rank
Hospitalizations(%ofpeak)
Masks
No
Yes
Governor
aa
Democratic
Republican
Current hospitalizations as a percent of peak since February
p masks as of July 20, 2020: 0.0095, p governor: 0.046. NB: association != causation.
2020-08-29 Summary: 32
33. Hospitalizations trends
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
min
max
min
max
min
max
min
max
min
max
min
max
min
max
min
max
Hospitalizationsfrommintomax
Hospitalizations trends from min to max
2020-08-29 Summary: 33
34. Change in hospitalizations over past 14
days
HI
DE
MT
KS
SD
IA
ND
NE
WV
AK
WY
CT
MO
IL
MN
DC
RI
OK
IN
MI
NC
VT
VA
WI
KY
WA
AR
PA
ID
NY
GA
OH
MD
MA
ME
CA
NJ
CO
TN
SC
NV
AL
MS
FL
OR
LA
TX
UT
AZ
NH
NM
-6.0
-3.0
0.0
3.0
1 6 11 16 21 26 31 36 41 46 51
Rank
Changeinhospitalizations(%/day)
Masks
No
Yes
Governor
aa
Democratic
Republican
Change in hospitalizations over past 14 days
p masks as of July 20, 2020: 0.57, p governor: 0.53. NB: association != causation.
2020-08-29 Summary: 34
35. Change in New Cases per Day
Direction
Increasing > +2%
Increasing between +0.5% and +2%
No Change (-0.5% to +0.5%)
Decreasing between -0.5% and -2%
Decreasing > -2%
NA
Trends by county as of 2020-08-29
NA = Inadequate data
2020-08-29 Summary: 35
36. Percent Change by Partisan Lean
-10
-5
0
5
10
0 25 50 75 100
Percent Republican
Percentchangeinnewcasesperday
25
50
75
Republican
Counties by 2016 presidential election results
Dark green line is a Friedman's supersmoother
2020-08-29 Summary: 36
37. Percent Change by Population
-10
-5
0
5
10
1,000 10,000 100,000 1,000,000 10,000,000
Population
Percentchangeinnewcasesperday
25
50
75
Republican
Counties by Population
Dark green line is a Friedman's 'super smoother'
2020-08-29 Summary: 37
38. Cases as a Percent of Population
0.001%
0.01%
0.1%
1%
10%
20%
1,000 10,000 100,000 1,000,000 10,000,000
County Population
Totalcases
Total Cases as a Percent of County Population
Slanted lines are counties with small integer numbers of cases, green line: Friedman's 'super smoother'
2020-08-29 Summary: 38
39. Deaths as a Percent of Population
0.0001%
0.001%
0.01%
0.1%
1%
1,000 10,000 100,000 1,000,000 10,000,000
County Population
Totaldeaths
Total Deaths as a Percent of County Population
Slanted lines are counties with small integer numbers of cases, green line: Friedman's 'super smoother'
2020-08-29 Summary: 39
40. Case Mortality vs. Population
0.1%
1%
10%
100%
1,000 10,000 100,000 1,000,000 10,000,000
County Population
Casemortality
Case Mortality vs. County Population
2020-08-29 Summary: 40